Question

Margo draws a triangle. The lengths of the sides of the triangle are 8", 15" and 17". Margo uses the area of 3 squares to show that the triangle is a right triangle. Which of these could be the area, in square units, of a square that Margo uses?

A. 32
B. 34
C. 46
D. 64

Answer 1

From the given options 64 units is the area of square that Margo used. So, option D is correct.

SOLUTION:

Given, Margo draws a triangle. The lengths of the sides of the triangle are
`8^(\prime \prime), 15^(\prime \prime) \text { and } 17^(\prime \prime)`

Margo uses the area of 3 squares to show that the triangle is a right triangle. We have to find the area, in square units, of a square that Margo uses . Now, we know that, we can prove a triangle as right angled triangle using Pythagoras theorem

`\text { Pythagoras theorem } \rightarrow \text { hypotenuse }^(2)=\text { side }^(2)+\text { side }^(2)`

Assume that above theorem is equation of area of one square = sum area of two squares. Then, using area of three squares we can prove that a triangle is a right angle triangle.

Now, areas of the three squares will be
`8^(2), 15^(2), 17^(2) \rightarrow 64,225,289`